1. Field of the Invention
The present invention relates generally to optical projection lithography methods and photolithography, and particularly to fluoride crystals with minimal spatial dispersion for use in optical photolithography systems utilizing ultraviolet light (UV) wavelengths below 200 nm, such as UV lithography systems utilizing wavelengths in the 193 nm region and the 157 nm region.
2. Technical Background
Projection optical photolithography methods/systems that utilize the ultraviolet wavelengths of light below 200 nm provide benefits in terms of achieving smaller feature dimensions. Such methods/systems that utilize ultraviolet wavelengths in the 157 nm and the 193 nm wavelength regions have the potential of improving the manufacturing of integrated circuits with smaller feature sizes. The commercial use and adoption of below 200 nm UV in high volume mass production of integrated circuits hinges on the availability of economically manufacturable optical fluoride crystals with high quality optical performance.
Fluoride crystals for use below 200-nm must have high internal transmission at the use wavelength ( greater than 98%/cm), high index of refraction homogeneity ( less than 2 ppm) and low residual stress birefringence ( less than 3 nm/cm). Stress birefringence is a consequence of the manufacturing process and can be minimized through careful annealing of the crystal. While the crystals typically used for these applications are cubic and so exhibit symmetric properties with respect to the crystal axes, they are not isotropic as for example, glass is. This distinction becomes clear when addressing a property called xe2x80x9cspatial dispersionxe2x80x9d. Spatial dispersion is a property that is described as the presence of birefringence that is dependent on the direction of light propagation. Glass (an isotropic material) has no such dependence. In cubic crystals such as Ge, Si and GaP, however, there is such a dependence that is found to exhibit 1/xcex2 variation with wavelength (Optical Anisotropy of Silicon Single Crystals, by J. Pastrnak and K. Vedam, PHYSICAL REVIEW B, VOLUME 3, NUMBER 8, APR. 15, 1971, p. 2567-2571;COMPUTATIONAL SOLID STATE PHYSICS, by Peter Y. Yu and Manuel Cardona, Plenum Press, N.Y., edited by F. Herman, 1972; Spatial Dispersion In The Dielectric Constant of GaAs, by Peter Y. Yu and Manuel Cardona, SOLID STATE COMMUNICATIONS, VOLUME 9, NUMBER 16, Aug. 15, 1971, pp.1421-1424). The effect we are describing, spatial dispersion, is absent from the dielectric response of a cubic crystal in the limit in which the wavelength of light, xcex, is much larger than the spacing between atoms. As the wavelength becomes smaller, additional terms in the dielectric response are no longer negligible. In a cubic crystal, inversion symmetry of the crystal structure only allows the first nonzero contribution to occur at order 1/xcex2 and not order 1/xcex. There is a mathematical description of dielectric response and crystal symmetry that uses tensors and their transformations to describe how dielectric response (including spatial dispersion) can depend on the direction of light propagation. Dielectric response is described using a rank 2 tensor, denoted xcex5ij. The lowest order effects of spatial dispersion can be described by a rank 4 tensor, here denoted xcex1ijkl, from the relation             ϵ      ij        ⁡          (              q        →            )        =                    ϵ        ij            ⁡              (                              q            →                    =          0                )              +                  ∑        kl            ⁢                        α          ijkl                ⁢                  q          k                ⁢                              q            l                    .                    
Here the symbol {right arrow over (q)} represents the wavevector of light; it points in the direction of light propagation and its magnitude is             2      ⁢      π        λ    .
The equation shows that the long-wavelength or {right arrow over (q)}=0 part of the dielectric tensor gets corrected by the sum of elements of the xcex1ijkl tensor times the x-, y-, or z-components of the wavevector. (The sum on k and l is a sum over cartesian directions x, y, and z.) This correction term represents the source of spatial dispersion. In the absence of this term, a cubic crystal would have a completely isotropic dielectric tensor xcex5ij and hence no spatial dispersion. Of the possible 3xc3x973xc3x973xc3x973=81 terms in the xcex1ijkl tensor, only 3 are nonzero and distinct in a cubic crystal with m3m symmetry, such as zincblende or fluorite structure crystals. It is known that rank 4 tensors have 3 tensor invariants. In fully isotropic systems such as glass, the tensor xcex1ijkl can only have 2 independent nonzero elements, and obeys the relation
(xcex11111xe2x88x92xcex11122)/2xe2x88x92xcex11212=0. 
The independent nonzero elements can be taken as xcex11111 and xcex11122. In a cubic system with m3m symmetry, the relation above need not be satisfied, and there are 3 independent nonzero elements of xcex1ijkl. These may be taken as xcex11111, xcex11122, and xcex11212. Since the first two tensor invariants are present in isotropic glasses, they cannot impart any anisotropy. Thus all anisotropy from spatial dispersion in cubic crystals is associated with the relation
(xcex11111xe2x88x92xcex11122)/2xe2x88x92xcex11212xe2x89xa00. 
The value of this combination of tensor elements in a cubic system sets the scale for all anisotropic optical properties associated with spatial dispersion. These constants themselves depend on the wavelength of light with a variation that is typical of index dispersion, i.e. much less variation with wavelength than the explicit 1/xcex2. This invention shows how to design a material in which (xcex11111xe2x88x92xcex11122)/2xe2x88x92xcex11212 is minimized or preferably zero at a given wavelength of design.
Calcium fluoride, a potential material for use in UV lithography systems, also exhibits spatial dispersion. Spatial dispersion is an inherent property of the crystal and as such cannot be reduced by processing such as annealing. Stress-induced birefringence and spatial dispersion birefringence can be distinguished by their respective wavelength dependences. The variation of spatial dispersion with wavelength is very strong compared with the variation in index of refraction or stress-induced birefringence with wavelength, with stress birefringence exhibiting roughly the dependence expected for simply the index of refraction and spatial dispersion having 1/xcex2 dependence.
Birefringence, whether it is derived from stress or the spatial properties of the crystal, can have a detrimental effect on high performance optical systems. The formation of multiple images is a major concern. Phase front distortion also presents problems both in terms of imaging and metrology. Given the wavelength dependence of spatial dispersion and the bandwidth of the lasers, dispersion becomes an important issue. It is thus of importance to minimize the amount of birefringence in a material for use in high performance optical imaging systems. As was mentioned previously, stress-related birefringence can be minimized by processing (annealing) while spatial dispersion is an inherent property that must be addressed in a different manner. One approach to the problem is to prepare mixed crystals that have minimized spatial dispersion; this is a single cubic fluoride crystal that contains 2 or 3 different alkaline earth metal cations that can deliver minimized spatial dispersion. This approach recognizes that the spatial birefringence of a given crystal is largely determined by the polarizability of the cation, by analogy with the Si and Ge crystals mentioned earlier. Specifically, we utilize a change in sign of the intrinsic birefringence for SrF2, CdF2, or BaF2 relative to CaF2 based on trends in polarizability.
The present invention includes an UV lithography method. The lithography method includes providing a radiation source with wavelength below 200-nm. The method includes providing cubic fluoride crystal optical elements having minimal spatial dispersion. The cubic fluoride crystals are comprised of a combination of alkaline earth cations having different optical polarizabilities such as to produce an overall isotropic polarizability that minimizes the fluoride crystal spatial dispersion below 200 nm. The rationale for producing the mixed crystal is based on the fact that the wavelength dependence of the dielectric tensor is expected to scale roughly with its wavelength-independent value, based on the quantum mechanical expressions for both cases. This means that more polarizable ions, with larger index of refraction, are also expected to contribute more to spatial dispersion. Some indication of this expected trend can be seen in the following table. For cubic crystal structures, the Clausius-Mossotti equation is valid, i.e.,             (                        n          2                -        1            )              (                        n          2                +        2            )        =                    4        ⁢        π            3        ⁢          ∑                        N          j                ⁢                  α          j                    
where n is the refractive index, and Nj is the concentration of ions of type j characterized by the electronic polarizability xcex1j. A total molecular polarizability can be defined as
xcex1xcexa3VmolNjxcex1j 
where Vmol is the volume per molecule. In cubic fcc crystals such as fluorite, Vmol=a3/4 where a is the cubic lattice constant. This allows us to solve for the molecular polarizability as   α  =                    3        ⁢                              a            3                    ⁡                      (                                          n                2                            -              1                        )                                      16        ⁢                  π          ⁡                      (                                          n                2                            +              2                        )                                .  
Given lattice constants and indices of refraction for several cubic materials, the following table can be computed:
In this table, the last column xcex94nxc3x97107 is the measured value of intrinsic birefringence for these materials. The clear trend among cubic semiconductors relates the magnitude of xcex94n and the molecular polarizability xcex1. Similarly, the trend in molecular polarizability among the cubic fluorides is considered. CaF2 has the lowest. The trend of xcex94n with polarizability suggests that any of the other cubic fluorides will have a xcex94n with a more positive value, enough to overcome the xe2x88x9211 value and ultimately drive to overall positive values of xcex94n.
Molecular polarizabilities are described in the above discussion however it is recognized that ionic polarizabilities of the cations can be used to formulate this discussion as well. All of the materials have the same ratio of cation to anion and have the same anion. A cubic crystal that incorporates an appropriate ratio of alkaline earth cations yields a material having minimized spatial dispersion.
The invention includes a fluoride crystal having a minimized amount of spatial dispersion. The fluoride combination crystal has a cubic fluoride crystal molecular structure and is comprised of a plurality of first alkaline earth metal cations and a plurality of second alkaline earth metal cations and a plurality of third alkaline earth metal cations. The first alkaline earth metal cations have a high polarizability and the second alkaline earth metal cations have a low polarizability. The appropriate combination of the first, second, and third alkaline earth metal cations in the fluoride crystal yields a crystal exhibiting minimized spatial dispersion.